{"paper":{"title":"A symmetric mechanism for symmetry-breaking in oscillator networks with strong nonlinear coupling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Theodore Vo, Yangyang Wang","submitted_at":"2026-06-16T10:57:33Z","abstract_excerpt":"In this article, we describe and analyse a novel mechanism for symmetry-breaking in minimal symmetrically coupled identical slow/fast oscillator networks with strong nonlinear mutually inhibitory coupling. We show that the symmetry-breaking, surprisingly, originates from the canard dynamics of a folded node that lies on the axis of symmetry. By applying geometric singular perturbation theory and the blow-up technique to a normal form, we determine the geometric mechanisms by which the {\\em symmetric folded node} induces symmetry-breaking. More specifically, we show that (i) the fold curve of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17780","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.17780/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}